[EM] Scientific American and the "Perfect Electoral System"

[Richard Lung]

“still keeping some degree of local representation”

“Local representation” by National Members is the mantra of Safe-seat 
Man, feeding the populus, reformers and anti-reformers alike, with their 
mothers milk, in which the most elementary logic plays no part.

Local representation is the prerogative of local government. National 
representation is the prerogative of national government, and not local 
representation.

The outcome of this cross-wired politics is that British local 
government is moribund, and members of the national parliament grossly 
over-burdened with relatively petty local problems; “glorified social 
workers,” far beyond their numbers to efficiently cope.

While, there is no time for the issues of national politics, which are 
corralled by the national executive, and in which the public has 
virtually no say, and is not expected to have. Hence the Hailsham term 
for the UKgovernment as “an elective dictatorship.”

Moreover the supposedly “local” representation of the single-member 
system is a euphemism for what actually takes place. In most cases, and 
as a matter of principle, these unstable constituencies do not serve any 
particular locality. Their boundaries are periodically smashed to give 
Members of Parliament an approximately equal workload and equal powers 
of patronage over their constituents. Neither democracy nor community is 
the purpose of the single-member system, but members monopolies on 
representation. The house of commons or communities should accurately be 
called the house of monopolies, departing from its historic role, late 
in the nineteenth century.

The assumption that the single-member constituency is the most local is 
the fallacy of scale. It is an extension of the confused idea that the 
only democracy is personal democracy, on the scale of the ancient Greek 
polis or city state.

In other words, democracy is not a function of representation by the 
fewest seats per constituency possible; one sole representative, 
democracy is, as Hare and Mill said it was, a function of many seats per 
constituency equally representative (by quota). This applies as much to 
the most local representation as to the most universal representation.

Regards,

Richard Lung.


On 09/11/2023 16:25, Toby Pereira wrote:
> On non-deterministic methods, they can give potentially a better level 
> of proportional representation than deterministic methods, while still 
> keeping some degree of local representation. If you have 
> constituencies with 5 or 6 representatives and use e.g. STV, then 
> parties/ideologies with 10% of the support nationally would likely 
> keep missing out and win far less than 10% of the seats. 
> Non-deterministic methods can mean that on average things balance out.
>
> If you use the simple random ballot method, things would still be 
> pretty bad. With just one representative per constituency, quite a lot 
> of people are likely to be represented only by a lunatic fringe 
> candidate. But with 5 or 6 winning candidates, popular candidates will 
> still generally win through, and there will be a balance of 
> representation in each constituency.
>
> Proportional methods can also get quite complex, but this can be 
> massively reduced with a non-deterministic method. For example, COWPEA 
> Lottery uses approval voting. To elect candidates you simply do this:
>
> Start with a list of all currently-unelected candidates. Pick a ballot 
> at random and remove from the list all candidates not approved on this 
> ballot. Pick another ballot at random, and continue with this process 
> until one candidate is left. Elect this candidate. If the number of 
> candidates ever goes from >1 to 0 in one go, ignore that ballot and 
> continue. If any tie cannot be broken, then elect the tied candidates 
> with equal probability.
>
> It also has very good criterion compliance. If you accept 
> non-determinism and ballots that aren't just ordinal, then probably 
> the best of any known candidate-based proportional method. 
> https://electowiki.org/wiki/COWPEA
>
> Toby
>
> On Wednesday, 8 November 2023 at 18:18:24 GMT, Richard Lung 
> <voting at ukscientists.com> wrote:
>
>
>
> Why has theorem Arrow gained so much traction over the years?
>
> The short answer, history is written by the victors.
>
> The history answer takes some explaining but is evident enough.
>
> New York, for instance, had a Personal Representation society, by the 
> late nineteenth century. In fact the organised campaign writings, of 
> its early successes, over a century old, have been bought-up, and are 
> still subject to publishers pay walls, of little if any commercial 
> value and contrary to the public interest.
>
> By the 1937 edition of Proportional Representation. The key to 
> democracy. Clarence Hoag and George Hallett were introducing a single 
> transferable vote to the boroughs of New York.
>
> These two campaigning great men, both mathematicians in their day job, 
> did not get a mention in Wikipedia, when I last looked.
>
> As a result of battering-ram referendums with the money and publicity 
> on their side, The Machine virtually abolished the key to democracy.
>
> Massachusettslegislature forbad other cities than Cambridgeto use 
> their electoral reform. There are several home-rule bills but they are 
> bogged down in state committee.
>
> Kenneth Arrow stepped in, in the nineteen fifties, to effectively 
> finish the job of The Machine. He took the Kurt Godel Incompleteness 
> theorem an extreme step further by advertising an “Impossibility 
> theorem,” which he himself, cited in Scientific American, belatedly 
> admitted it did not amount to.
>
> In other words, he by-passed, nearly a century of election method 
> study, stemming from Thomas Hare and John Stuart Mill. That tradition 
> continues and so does the naïve ignorance of it.
>
> As a Scottish STV programmer commented, theorem Arrow does not even 
> apply to proportional representation, but merely to bare majority 
> elections.
>
> Any theorem is only as good as its assumptions, and those of the 
> Impossibility theorem neglect the possibility that statistical methods 
> might be more accurate than deterministic ones, as is indeed the case 
> in physics.
>
> Regards,
>
> Richatrd Lung.
>
>
>
>
> On 07/11/2023 13:35, Toby Pereira wrote:
>> As is often the case, I think the importance of Arrow's Theorem is 
>> overstated in that article. Arrow's Theorem essentially says "With a 
>> few reasonable background assumptions, no ranked-ballot method passes 
>> Independence of Irrelevant Alternatives." But this was already known 
>> for centuries from the Condorcet Paradox. I don't really know why 
>> it's gained so much traction over the years, as it was nothing like 
>> the paradigm shift people credit it as.
>>
>> Toby
>>
>> On Tuesday, 7 November 2023 at 04:29:31 GMT, Forest Simmons 
>> <forest.simmons21 at gmail.com> <mailto:forest.simmons21 at gmail.com> wrote:
>>
>>
>> Rob,
>>
>> Thanks for clearing up a lot  of the confusion... and for putting the 
>> current status in perspective.
>>
>> I like the comparison of the "impossibilities of voting" with the 
>> impossibilities of faster than light travel, etc.  The 2nd law of 
>> thermodynamics is especially relevant... because as Prigogene showed 
>> in the 70's, the impossibility of decreasing entropy in closed 
>> systems still allows for local pockets of possibility ... that make 
>> life possible .... until the "heat death" of our island space-time 
>> big bang remnant ... while miriads of new "inflationary bubbles" 
>> appear from random virtual quantum fluctuations.
>>
>> We used to "know" that the event horizon was a boundary of no return 
>> .... nut now evaporation of black holes through quantum tunneling is 
>> taken for granted.
>>
>> In the early 1800's Gauss proved the impossibility of trisecting an 
>> arbitrarily given angle .... inside the rules of classical geometric 
>> ruler and compass constructions.
>>
>> But it turns out that (as any first year topology student can show) 
>> any angle can be transformed into atrisectable one by an arbitrarily 
>> small perturbation.
>>
>> I'm fact, once you learn the binary point expansion of 1/3 ..., you 
>> can get within a relative error tolerance of 1/2^n precision with n 
>> bisections... bisections being the first constructions you learn in 
>> geometty.
>>
>> Pockets of possibility like these .... adequate "For All Practical 
>> Purposes" pervade mathematics ... including the mathematics of voting 
>> systems.
>>
>> Sometimes you have to discover new tools not included in the 
>> classical tool kit. In  the case of angle trisections, if you are 
>> allowed to make a few marks on the ruler... hen the general ruler and 
>> compass trisection suddenly resolves itself.
>>
>> Thanks,
>>
>> Forest
>>
>> On Sun, Nov 5, 2023, 11:34 PM Rob Lanphier <roblan at gmail.com 
>> <mailto:roblan at gmail.com>> wrote:
>>
>>     Hi folks,
>>
>>     I just wrote a letter to the editor(s) of Scientific American,
>>     which I've included below.  My letter was in a response to the
>>     following article that was recently published on their website:
>>     https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/
>>     <https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/>
>>
>>     Y'all may have other thoughts on the article.
>>
>>     Rob
>>     ---------- Forwarded message ---------
>>     From: *Rob Lanphier* <roblan at gmail.com <mailto:roblan at gmail.com>>
>>     Date: Sun, Nov 5, 2023 at 11:22 PM
>>     Subject: Regarding using math to create a "Perfect Electoral System"
>>     To: Scientific American Editors <editors at sciam.com
>>     <mailto:editors at sciam.com>>
>>
>>
>>     To whom it may concern:
>>
>>     I appreciate your article "Could Math Design the Perfect
>>     Electoral System?", since I agree that math is important for
>>     understanding electoral reform, and there's a lot of good
>>     information and great diagrams in your article:
>>     https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/
>>     <https://www.scientificamerican.com/article/see-how-math-could-design-the-perfect-electoral-system/>
>>
>>     There's some things that the article gets wrong, but the good
>>     news is that the article title and its relation to Betteridge's
>>     law.  This law states "Any headline that ends in a question mark
>>     can be answered by the word /'/no/'/." The bad news: the URL slug
>>     ("see-how-math-could-design-the-perfect-electoral-system")
>>     implies the answer is "yes".  The answer is "no"; Kenneth Arrow
>>     and Allan Gibbard proved there is no perfect electoral system
>>     (using math).
>>
>>     I appreciate that your article highlights the mayoral election in
>>     Burlington, Vermont in 2009.  That is an important election for
>>     all voters considering FairVote's favorite single-winner system
>>     ("instant-runoff voting" or rather "ranked-choice voting, as they
>>     now call it).  When I volunteered with FairVote in the late
>>     1990s, I remember when they introduced the term "instant-runoff
>>     voting".  I thought the name was fine.  After Burlington 2009, it
>>     would seem that FairVote has abandoned the name.  Regardless,
>>     anyone considering instant-runoff needs to consider Burlington's
>>     experience.
>>
>>     Sadly, your article describes "cardinal methods" in a confusing
>>     manner.  It erroneously equates cardinal's counterpart ("ordinal
>>     voting") with "ranked-choice voting". Intuitively, all "ordinal
>>     methods" should be called "ranked choice voting", but during this
>>     century, the term has been popularized by FairVote and the city
>>     of San Francisco to refer to a specific method formerly referred
>>     to as "instant-runoff voting". These days, when Americans speak
>>     of "RCV", they're generally referring to the system known on
>>     English Wikipedia as "IRV" (or "Instant-runoff voting"):
>>     https://en.wikipedia.org/wiki/Instant-runoff_voting
>>     <https://en.wikipedia.org/wiki/Instant-runoff_voting>
>>
>>     There have been many methods that use ranked ballots, including
>>     the methods developed by Nicolas de Condorcet and Jean-Charles de
>>     Borda in the 1780s and the 1790s. I'm grateful that the Marquis
>>     de Condorcet's work is featured so prominently in your article. 
>>     Condorcet's work was brilliant, and I'm sure he would have become
>>     more prominent if he hadn't died in a French prison in the
>>     1790s.  Many single-winner methods that strictly comply with the
>>     "Condorcet winner criterion" are probably as close to "perfect"
>>     as any system (from a mathematical perspective).
>>
>>     Most methods that pass the "Condorcet winner criterion" typically
>>     use ranked ballots (and thus are "ordinal"), but it's important
>>     to note that almost all "ordinal" methods can use cardinal
>>     ballots. Instant-runoff voting doesn't work very well with
>>     cardinal ballots (because tied scores cannot be allowed), but
>>     most other ordinal systems work perfectly well with tied ratings
>>     or rankings.  Even though passing the Condorcet winner criterion
>>     is very important, there are many methods that come very, very
>>     close in reasonable simulations.  I would strongly recommend that
>>     you contact Dr. Ka-Ping Yee, who is famous in electoral reform
>>     circles for "Yee diagrams":
>>     https://electowiki.org/wiki/Yee_diagram
>>     <https://electowiki.org/wiki/Yee_diagram>
>>     (a direct link to Yee's 2005 paper: http://zesty.ca/voting/sim/
>>     <http://zesty.ca/voting/sim/> )
>>
>>     Note that "approval voting" and "Condorcet" provide pretty much
>>     the same results in Yee's 2005 paper.  "Instant-runoff voting"
>>     seems a little crazy in Yee's simulations.
>>
>>     Though Arrow and Gibbard disproved "perfection", I prefer to
>>     think of Arrow's and Gibbard's work as defining the physics of
>>     election methods.  To explain what I mean, consider the physics
>>     of personal transportation.  It is impossible to design the
>>     PERFECT vehicle (that is spacious, and comfortable, travels
>>     faster than the speed of light, fits in anyone's garage or
>>     personal handbag).  Newton and Einstein more-or-less proved it. 
>>     However, those esteemed scientists' work didn't cause us to stop
>>     working on improvements in personal transportation.  Buggy whips
>>     are now (more or less) recognized as obsolete, as is Ford's
>>     "Model T".
>>
>>     Now that Arrow and Gibbard have helped us understand the physics
>>     of election methods, we can hopefully start pursuing alternatives
>>     to the buggy whip (or rather, alternatives to "choose-one" voting
>>     systems, often referred to as "first past the post" systems).
>>
>>     This gets me to the statement from your article that gets under
>>     my skin the most::
>>
>>         This is called cardinal voting, or range voting, and although
>>         it’s no panacea and has its own shortcomings, it circumvents
>>         the limitations imposed by Arrow’s impossibility theorem,
>>         which only applies to ranked choice voting.
>>
>>     People who study election methods refer to "cardinal voting" as a
>>     /category/ of voting methods, of which "range voting" is just one
>>     (which is called "score voting" on English Wikipedia):
>>     https://en.wikipedia.org/wiki/Score_voting
>>     <https://en.wikipedia.org/wiki/Score_voting>
>>
>>     The conflation of "ranked choice voting" with all ordinal voting
>>     methods is also highly problematic (though I don't entirely blame
>>     you for this).  As I stated earlier, there are many methods that
>>     can use ranked ballots.  While this article may have been helpful
>>     for those of us that prefer ranking methods that are not
>>     "instant-runoff voting" back when FairVote switched to
>>     "ranked-choice voting" in the early 2010s. Note that before the
>>     fiasco in Burlington in 2009, FairVote pretty consistently
>>     preferred "instant runoff voting":
>>     https://web.archive.org/web/20091111061523/http://www.fairvote.org/
>>     <https://web.archive.org/web/20091111061523/http://www.fairvote.org/>
>>
>>     I appreciate that you're trying to explain this insanely
>>     complicated topic to your readers.  When I edit English Wikipedia
>>     (which I've done for over twenty years), I would love to be able
>>     to cite Scientific American on this topic.  However, I'm not yet
>>     sure I'd feel good about citing this article.
>>
>>     Rob Lanphier
>>     Founder of election-methods mailing list and electowiki.org
>>     <http://electowiki.org>
>>     https://robla.net <https://robla.net>
>>     https://electowiki.org/wiki/User:RobLa
>>     <https://electowiki.org/wiki/User:RobLa>
>>     https://en.wikipedia.org/wiki/User:RobLa
>>     <https://en.wikipedia.org/wiki/User:RobLa>
>>
>>     p.s. back in the late 1990s, I wrote an article for a small tech
>>     journal called "The Perl Journal". It's out of print, but I've
>>     reproduced my 1996 article about election methods which I think
>>     holds up pretty well:
>>     https://robla.net/1996/TPJ <https://robla.net/1996/TPJ>
>>     ----
>>     Election-Methods mailing list - see https://electorama.com/em
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>>
>> ----
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